Question

Calculate the distance between the points (7, 4) and (-5, -3).​

Answer 1

D = √193 units

or

D = 13.892 units

Step-by-step explanation:

Given:

(7, 4) and (-5, -3)

Calculate the distance

Solution:

`\rm \: Distance (D) = \sqrt{( x_(2) - x_(1)) {}^(2) + (y_(2) - y_{1) {}^(2) }}`

Now, substitute the values given:

`\rm \: D = \sqrt{ \{( - 5) - 7 \}^(2) + \{( - 3) - 4 {}^{} \} {}^(2) }`

`\rm \: D = \sqrt{ \{12 \}^(2) + \{( - 3) - 4 {}^{} \} {}^(2) }`

`\rm \: D = \sqrt{ 144 + \{( - 3) - 4 {}^{} \} {}^(2) }`

`\rm D = \sqrt{144 + \{ 7\}{}^(2) }`

`\rm \: D = √(144 + 49)`

`\boxed{\rm \: D = √(193)}`

`\boxed{\rm \: D =13 .892}`

Thus, Distance between the two given points will be √193 or √13.892 units.

Answer 2

`\bf √(193)` units or 13.9 units is the distance.

Step-by-step explanation:

`\sf Distance \ between \ two \ points = √((x_2 - x_1)^2 +(y_2 - y_1)^2)`

Given points: (7, 4) and (-5, -3)

Identify following:

`\sf x_2= 7`,
`\sf x_1 = -5`,
`\sf y_2 =4`,
`\sf y_1 =-3`

Find distance:

`\rightarrow \sf √((7 - (-5))^2 + (4 - (-3))^2) \quad = \quad √(144+49) \quad = \quad √(193) \quad \approx \ 13.9`